Staircases: a lesson which can work in different ways and yield different payoffs at various levels: pre-algebra, Algebra 1, Algebra 2, Teachers' Mathematics. I link to it here because it can serve as a preview of arithmetic series. (There are detailed notes and some spoilers on pp. 2-3.)
- Lessons from Algebra: Themes, Tools, Concepts by Anita Wah and Henri Picciotto
- Arithmetic Sequences and Series | Teacher notes
- Geometric Sequences and Series | Teacher notes
- Nested Squares
Part of the pedagogy behind the above lessons:
- From my Math Education Blog:
- Geometric in More Than One Way!
- An unusual but effective Algebra 2 introduction to sequences:
- Iterating Linear Functions
- Lessons for 11th and 12th grade about triangular, pentagonal, and Fibonacci numbers:
- Stairway to Infinity! Proof by Mathematical Induction
- Directory of material on this site that involves integer sequences, with links to the Online Encyclopedia of Integer Sequences:
- Integer Sequences